Notes on non-archimedean topological groups

Michael Megrelishvili, Menachem Shlossberg

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We show that the Heisenberg type group HX=(Z2⊕V){left semidirect product}V*, with the discrete Boolean group V:=C(X,Z2), canonically defined by any Stone space X, is always minimal. That is, H X does not admit any strictly coarser Hausdorff group topology. This leads us to the following result: for every (locally compact) non-archimedean G there exists a (resp., locally compact) non-archimedean minimal group M such that G is a group retract of M. For discrete groups G the latter was proved by S. Dierolf and U. Schwanengel (1979) [6]. We unify some old and new characterization results for non-archimedean groups.

Original languageEnglish
Pages (from-to)2497-2505
Number of pages9
JournalTopology and its Applications
Volume159
Issue number9
DOIs
StatePublished - 1 Jun 2012

Bibliographical note

cited By 2

Keywords

  • Boolean group
  • Heisenberg group
  • Isosceles
  • Minimal group
  • Non-archimedean group
  • Stone duality
  • Stone space
  • Ultra-metric

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